edit: aargh! sorry @drehb, I didn't see you've already replied.
Good questions! I forgot to mention the idea of hardware wallets is isolation from the possibly infected operating system of a p.c. or mobile (cell phone). They also tend to have screens and hardware buttons so that transaction information can be safely verified.
I won't say that the security of hardware wallets is perfect, because with enough resources people come up with some very clever ways of hacking things. It's soooo much more secure than general software wallets though. Here is more detail about some aspects which spring to mind:
Hardware wallets (HW wallets) isolate the private keys from your desktop or mobile operating system. When you carry out a transaction it is the HW wallet which signs the transaction, using the private keys contained within. The signed transaction can be safely passed to the software wallet because it cannot be tampered with. The cryptography involved means that amounts, addresses et cetera cannot be adjusted.
On a good HW wallet the amount and the addresses have to be verified before the transaction is signed. For example on the Nano S there is a screen which shows you this information, and you must use the hardware buttons on the HW wallet to confirm. Again, this is isolated from the general operating system for security. Software wallets are vulnerable here. For example there are reports that there is malware which on Windows can monitor the clipboard, looking for bitcoin addresses. It can replace an address with one belonging to the attacker, therefore stealing money. I think it can even hide, in the UI, that it has changed the address!
The hardware buttons on the HW wallet also have to be used when entering the PIN or the wallet passphrase. This should avoid the keyloggers which are so dangerous with software wallets.
I think it could be worded better, but it's hard to convey information concisely sometimes. It's possibly more difficult for the LedgerWallet team because it's a French company.
I'd agree there's little practical difference. You do have to trust the hardware and it's firmware though. I need to look into whether or not there are good ways to verify the integrity. With a new device I would do small test transactions for starters. When generating keys for paper wallets the software should be verified too. (Is there anyone attempting to generate keys by hand by the way? I wonder how long this would take?!).
You've got the gist.
By the way I feel like a fraud! I'm a manual worker. I don't even know how any programming languages. I have intended to learn for years, but I STILL haven't done it. How lame!...
Still trust my information?